Bundle - Wikipedia

Bundle - Wikipedia: "Bundle (mathematics), a generalization of a fiber bundle dropping the condition of a local product structure
Fiber bundle, a topology space that looks locally like a product space
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Derivation (differential algebra) - Wikipedia

Derivation (differential algebra) - Wikipedia: "The partial derivative with respect to a variable is an R-derivation on the algebra of real-valued differentiable functions on Rn. The Lie derivative with respect to a vector field is an R-derivation on the algebra of differentiable functions on a differentiable manifold; "



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Detexify LaTeX handwritten symbol recognition

Detexify LaTeX handwritten symbol recognition:



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Tangent space - Wikipedia

Tangent space - Wikipedia: "A real-valued function {\displaystyle f:M\to \mathbf {R} } is said to belong to {\displaystyle {C^{\infty }}(M)} if and only if for every coordinate chart {\displaystyle \varphi :U\to \mathbf {R} ^{n}} , the map {\displaystyle f\circ \varphi ^{-1}:\varphi [U]\subseteq \mathbf {R} ^{n}\to \mathbf {R} } is infinitely differentiable. "



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Tangent space - Wikipedia

Tangent space - Wikipedia: "This map turns out to be bijective and may be used to transfer the vector-space operations on {\displaystyle \mathbf {R} ^{n}} over to {\displaystyle T_{x}M} , thus turning the latter set into an {\displaystyle n} -dimensional real vector space."



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Volume

Volume - Wikipedia: "Integrating the volume form gives the volume of the manifold according to that form."



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Volume form - Wikipedia

Volume form - Wikipedia:



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Multilinear form - Wikipedia

Multilinear form - Wikipedia: "Given a basis {\displaystyle (v_{1},\ldots ,v_{n})} for {\displaystyle V} and its dual {\displaystyle (\phi ^{1},\ldots ,\phi ^{n})} for dual vector space {\displaystyle V^{*}={\mathcal {A}}_{1}(V)} , the wedge products {\displaystyle \phi ^{i_{1}}\wedge \cdots \wedge \phi ^{i_{k}}} , with {\displaystyle 1\leq i_{1}<\cdots

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One-form - Wikipedia

One-form - Wikipedia: "Gravitation"



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Linear map - Wikipedia

Linear map - Wikipedia: "Since the automorphisms are precisely those endomorphisms which possess inverses under composition, Aut(V) is the group of units in the ring End(V).
If V has finite dimension n, then End(V) is isomorphic to the associative algebra of all n × n matrices with entries in K. The automorphism group of V is isomorphic to the general linear group GL(n, K) of all n × n invertible matrices with entries in K.
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Linear map - Wikipedia

Linear map - Wikipedia: "If V has finite dimension n, then End(V) is isomorphic to the associative algebra of all n × n matrices with entries in K. The automorphism group of V is isomorphic to the general linear group GL(n, K) of all n × n invertible matrices with entries in K.
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Generalized function - Wikipedia

Generalized function - Wikipedia: "A further way in which the theory has been extended is as generalized sections of a smooth vector bundle. This is on the Schwartz pattern, constructing objects dual to the test objects, smooth sections of a bundle that have compact support. The most developed theory is that of De Rham currents, dual to differential forms. These are homological in nature, in the way that differential forms give rise to De Rham cohomology. They can be used to formulate a very general Stokes' theorem."



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Distribution (mathematics) - Wikipedia

Distribution (mathematics) - Wikipedia: "Distributions are a class of linear functionals that map a set of test functions (conventional and well-behaved functions) into the set of real numbers"



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Distribution (mathematics) - Wikipedia

Distribution (mathematics) - Wikipedia: "Distributions are a class of linear functionals that map a set of test functions (conventional and well-behaved functions) into the set of real numbers"



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Distribution (mathematics) - Wikipedia

Distribution (mathematics) - Wikipedia: "Distributions are a class of linear functionals that map a set of test functions (conventional and well-behaved functions) into the set of real numbers"



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Singleton (mathematics) - Wikipedia

Singleton (mathematics) - Wikipedia: "In the standard set-theoretic construction of the natural numbers, the number 1 is defined as the singleton { {\displaystyle \varnothing } }."



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Binomial coefficient - Wikipedia

Binomial coefficient - Wikipedia: " "n choose k""



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Gravitation (book) - Wikipedia

Gravitation (book) - Wikipedia: "vectors or one-forms,"



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Linear map - Wikipedia

Linear map - Wikipedia: "A linear map from {\displaystyle \mathbf {V} } to {\displaystyle \mathbf {K} } (with {\displaystyle \mathbf {K} } viewed as a vector space over itself) is called a linear functional.[5]

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Continuous symmetry - Wikipedia

Continuous symmetry - Wikipedia: "an intuitive idea corresponding to the concept of viewing some symmetries as motions,"



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Schwarzschild radius - Wikipedia

Schwarzschild radius - Wikipedia: "every quantity "



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Algebraic variety - Wikipedia

Algebraic variety - Wikipedia: "The fundamental theorem of algebra establishes a link between algebra and geometry by showing that a monic polynomial (an algebraic object) in one variable with complex number coefficients is determined by the set of its roots (a geometric object) in the complex plane. Generalizing this result, Hilbert's Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets. Using the Nullstellensatz and related results, mathematicians have established a strong correspondence between questions on algebraic sets and questions of ring theory. This correspondence is the specificity of algebraic geometry.

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Homogeneous polynomial - Wikipedia

Homogeneous polynomial - Wikipedia: "A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients,"



n-forms share being homogeneous with their field.

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Hamiltonian constraint - Wikipedia

Hamiltonian constraint - Wikipedia: "Hamiltonian constraint
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Hamiltonian constraint - Wikipedia

Hamiltonian constraint - Wikipedia: "Hamiltonian constraint
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Metric tensor (general relativity) - Wikipedia

Metric tensor (general relativity) - Wikipedia: "The flat space metric (or Minkowski metric) is often denoted by the symbol η and is the metric used in special relativity."



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